Problem: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 7)^2 - 1$
Answer: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 7)^2 - 1 = 0$ Add $1$ to both sides so we can start isolating $x$ on the left: $ (x - 7)^2 = 1$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 7)^2} = \pm \sqrt{1}$ Be sure to consider both positive and negative $1$ , since squaring either one results in $1$ $ x - 7 = \pm 1$ Add $7$ to both sides to isolate $x$ on the left: $ x = 7 \pm 1$ Add and subtract $1$ to find the two possible solutions: $ x = 8 \text{or} x = 6$